The explicit formula for Gauss-Jordan elimination applied to flexible systems

Detalhes bibliográficos
Autor(a) principal: Tran, Nam van
Data de Publicação: 2022
Outros Autores: Justino, Júlia, Berg, Imme van den
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.26/41075
Resumo: Flexible systems are obtained from systems of linear equations by adding to the elements of the coefficient matrix and the right-hand side scalar neutrices, which are convex groups of (non-standard) real numbers. The neutrices model imprecisions, giving rise to calculation rules extending informal error calculus. Stability conditions for flexible systems are given in terms of relative imprecision and size of determinants. We then apply the explicit formula for the elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure to find the solution of flexible systems, keeping track of the error terms at every stage. The solution respects the original imprecisions in the right-hand side and is the same as the one given by Cramer’s rule.
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spelling The explicit formula for Gauss-Jordan elimination applied to flexible systemsGauss-Jordan eliminationFlexible systemsStabilityExternal numbersFlexible systems are obtained from systems of linear equations by adding to the elements of the coefficient matrix and the right-hand side scalar neutrices, which are convex groups of (non-standard) real numbers. The neutrices model imprecisions, giving rise to calculation rules extending informal error calculus. Stability conditions for flexible systems are given in terms of relative imprecision and size of determinants. We then apply the explicit formula for the elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure to find the solution of flexible systems, keeping track of the error terms at every stage. The solution respects the original imprecisions in the right-hand side and is the same as the one given by Cramer’s rule.Repositório ComumTran, Nam vanJustino, JúliaBerg, Imme van den2022-06-15T11:14:19Z20222022-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.26/41075engTran, N., Justino, J. & Berg, I. (2022). The explicit formula for Gauss-Jordan elimination applied to flexible systems. Special Matrices, 10(1), 366-393. https://doi.org/10.1515/spma-2022-0168 Copy to clipboard BIBTE2300-745110.1515/spma-2022-0168info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-11-21T09:56:57Zoai:comum.rcaap.pt:10400.26/41075Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T23:12:25.446411Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv The explicit formula for Gauss-Jordan elimination applied to flexible systems
title The explicit formula for Gauss-Jordan elimination applied to flexible systems
spellingShingle The explicit formula for Gauss-Jordan elimination applied to flexible systems
Tran, Nam van
Gauss-Jordan elimination
Flexible systems
Stability
External numbers
title_short The explicit formula for Gauss-Jordan elimination applied to flexible systems
title_full The explicit formula for Gauss-Jordan elimination applied to flexible systems
title_fullStr The explicit formula for Gauss-Jordan elimination applied to flexible systems
title_full_unstemmed The explicit formula for Gauss-Jordan elimination applied to flexible systems
title_sort The explicit formula for Gauss-Jordan elimination applied to flexible systems
author Tran, Nam van
author_facet Tran, Nam van
Justino, Júlia
Berg, Imme van den
author_role author
author2 Justino, Júlia
Berg, Imme van den
author2_role author
author
dc.contributor.none.fl_str_mv Repositório Comum
dc.contributor.author.fl_str_mv Tran, Nam van
Justino, Júlia
Berg, Imme van den
dc.subject.por.fl_str_mv Gauss-Jordan elimination
Flexible systems
Stability
External numbers
topic Gauss-Jordan elimination
Flexible systems
Stability
External numbers
description Flexible systems are obtained from systems of linear equations by adding to the elements of the coefficient matrix and the right-hand side scalar neutrices, which are convex groups of (non-standard) real numbers. The neutrices model imprecisions, giving rise to calculation rules extending informal error calculus. Stability conditions for flexible systems are given in terms of relative imprecision and size of determinants. We then apply the explicit formula for the elements of the successive intermediate matrices of the Gauss-Jordan elimination procedure to find the solution of flexible systems, keeping track of the error terms at every stage. The solution respects the original imprecisions in the right-hand side and is the same as the one given by Cramer’s rule.
publishDate 2022
dc.date.none.fl_str_mv 2022-06-15T11:14:19Z
2022
2022-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10400.26/41075
url http://hdl.handle.net/10400.26/41075
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Tran, N., Justino, J. & Berg, I. (2022). The explicit formula for Gauss-Jordan elimination applied to flexible systems. Special Matrices, 10(1), 366-393. https://doi.org/10.1515/spma-2022-0168 Copy to clipboard BIBTE
2300-7451
10.1515/spma-2022-0168
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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